 COROLLARY. Tangents to a circle from the same external point are equal. For, connect the points of tangency, and two angles of the triangle are equal by this theorem. 198. The theorem is often stated thus: An angle formed by a tangent and a chord of a...  New Plane Geometry - Page 132by Wooster Woodruff Beman, David Eugene Smith - 1899 - 252 pagesFull view - About this book
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...ZBAC=£ZBOC. 4. .'. ZXAB =£ZAOB. 5. Also, ZCAX' = £ZCOA. 6. /.Z BAX' = iZ BOA. 3+5. Why? Ax. 3 Why? Ax. 2 COROLLARY. Tangents to a circle from the same...angles of the triangle are equal by this theorem. EXERCISES. 306. In the figure of th. 13, if P is the mid'point of arc AB, prove that P is equidistant... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...st. Z. 3. 4. 5. Also, 6. Why ? ZBAC=iZBOC. . ZXAB =AZ AOB. ZCAX'=4ZCOA. Z BOA. 3 + 5. Why? Ax. 3 Why? Ax. 2 COROLLARY. Tangents to a circle from the same...angles of the triangle are equal by this theorem. EXERCISES. 306. In the figure of th. 13, if P is the mid-point of arc AB, prove that P is equidistant... | |
 | Joe Garner Estill - 1896 - 214 pages
...any triangle, a line drawn parallel to the base divides the other sides proportionally. 3. Prove that an angle formed by a tangent and a chord of a circle meeting at the point of contact of the tangent, is measured by one-half of the included arc. B. 4.... | |
 | Joe Garner Estill - 1896 - 186 pages
...preparation. A. 1. Prove that, in a circle, a diameter is greater than any other chord. 3. Prove that an angle formed by a tangent and a chord of a circle meeting at the point of contact of the tangent, is measured by one-half of the included arc. B. 4.... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 412 pages
...Z.BAC =%^BOC, Why? .'. Z XAB = £ Z JO7?. Ax. 3 3. Also, v Z (L4JT = £ Z COJ, Why ? Ax. 2 Then 2. And COROLLARY. Tangents to a circle from the same external...theorem is often stated thus: An angle formed by a tan,r/ent and a chord of a. circle is measured by half its intercepted arc. See § 195. PROPOSITION... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 400 pages
...by the Law of Converse, § 73. Let the student write out the proof. PROPOSITION XIII. 197. Theorem. An angle formed by a tangent and a chord of a circle equals half of the central angle standing on the intercepted arc. X'C sB Given AB a chord, XX' a tangent... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1903 - 400 pages
...Z. Why ? 2. And -.' ZBAC =%^BOC, Why? .-. Z XAB = %^AOB. Ax. 3 3. Also, v Z CAX' = £ Z f'O.4, Why ? Ax. 2 COROLLARY. Tangents to a circle from the same...theorem is often stated thus : An angle formed by a taiigeiit and a chord of a circle is measured by half its intercepted arc. PROP. XIV.] CHORDS AND TANGENTS.... | |
 | Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...angles of an inscribed triangle are 75°, 95°. Find the arcs subtended by the sides. 210. Theorem VII. An angle formed by a tangent and a chord of a circle is measured by one half the arc subtended by the chord. Notice that there are two angles between the chord and the... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 250 pages
...circle may be circumscribed about the quadrilateral. Prove by reductio ad absurdum : 293. THEOREM. An angle formed by a tangent and a chord of a circle is equal to any inscribed angle subtended by the arc intercepted between the sides of the angle. APB FIG.... | |
 | United States. Office of Education - 1921 - 1286 pages
...right angle. 16. Parallel lines tangent to or cutting a circle intercept equal arcs on the circle. 17. An angle formed by a tangent and a chord of a circle is measured by half the intercepted arc. 18. An angle formed by two intersecting chords is measured by half the sum of... | |
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